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Mottl
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Hurst exponent evaluation and R/S-analysis in Python

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hurst

Hurst exponent evaluation and R/S-analysis

Python 2.7 Python 3x Build Status pypi Downloads

hurst is a small Python module for analysing random walks and evaluating the Hurst exponent (H).

H = 0.5 — Brownian motion,
0.5 < H < 1.0 — persistent behavior,
0 < H < 0.5 — anti-persistent behavior.

Installation

Install hurst module with

pip install hurst

or
pip install -e git+https://github.com/Mottl/hurst#egg=hurst

Usage

import numpy as np
import matplotlib.pyplot as plt
from hurst import compute_Hc, random_walk

Use random_walk() function or generate a random walk series manually:

series = random_walk(99999, cumprod=True)

np.random.seed(42) random_changes = 1. + np.random.randn(99999) / 1000. series = np.cumprod(random_changes) # create a random walk from random changes

Evaluate Hurst equation

H, c, data = compute_Hc(series, kind='price', simplified=True)

Plot

f, ax = plt.subplots() ax.plot(data[0], c*data[0]**H, color="deepskyblue") ax.scatter(data[0], data[1], color="purple") ax.set_xscale('log') ax.set_yscale('log') ax.set_xlabel('Time interval') ax.set_ylabel('R/S ratio') ax.grid(True) plt.show()

print("H={:.4f}, c={:.4f}".format(H,c))

R/S analysis

H=0.4964, c=1.4877

Kinds of series

The

kind
parameter of the
compute_Hc
function can have the following values:
'change'
: a series is just random values (i.e.
np.random.randn(...)
)
'random_walk'
: a series is a cumulative sum of changes (i.e.
np.cumsum(np.random.randn(...))
)
'price'
: a series is a cumulative product of changes (i.e.
np.cumprod(1+epsilon*np.random.randn(...)
)

Brownian motion, persistent and antipersistent random walks

You can generate random walks with

random_walk()
function as following:

Brownian

brownian = random_walk(99999, proba=0.5)

Brownian motion

Persistent

persistent = random_walk(99999, proba=0.7)

Persistent random walk

Antipersistent

antipersistent = random_walk(99999, proba=0.3)

Antipersistent random walk

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